Question

△ABC和△A'B'C'中,∠A∠B∠C所对的边分别是abc，∠A'∠B'∠C'所对的边分别是a'b'c'，∠A+∠B=∠C,∠B'+∠

△ABC和△A'B'C'中,∠A∠B∠C所对的边分别是abc，∠A'∠B'∠C'所对的边分别是a'b'c'，∠A+∠B=∠C,∠B'+∠C'=∠A'且b-a=b'-c',b+a=b'+c',则这两个三角形是否全等？证明

Answer 1

是全等的
首先我们来设几个等式 ∠A+∠B=∠C···················① ∠粗备B'+∠C'=∠A'···················②
b-a=b'-c'··················③ b+a=b'+c'·················④
证明：塌凳枣③+④得 2b=2b'，∴b=b'团拆
④-③得 2a=2c'，∴a=c'
又 ∠A+∠B+∠C=∠A'+∠B'+∠C'
将①和②代入得 2∠C=2∠A',∴∠C=∠A'
∠C为a，b的夹角，∠A'为b',c'的夹角
∴ΔABC全等于ΔC'B'A'

Answer 2

全等

Answer 3

a